It is sometimes known as differentiation under the integral sign.
This rule can be used to evaluate certain unusual definite integrals such as
for (Woods 1926).
Feynman (1997, pp. 69-72) recalled seeing the method in Woods (1926) and remarked "So because I was self-taught using that book, I had peculiar methods for doing integrals," and "I used that one damn tool again and again."
I think I'll put a square wave into an integrator...